# Thermodynamics: Calculating mass of air over a change in pressure/temperature

1. Apr 21, 2010

### MrNathan

1. The problem statement, all variables and given/known data

A vessel of capacity 3 m3 contains air at a pressure of 1.5 bar and a
temperature of 25o C. Additional air is now pumped into the system until the
pressure rises to 30 bar and temperature rises to 60o C. The molar mass of air
is 28.968 g/mol.

2. Relevant equations

Calculate:
(i) The mass of air pumped into the system.

3. The attempt at a solution

I am not sure of the equation i should be using. I thought i should be using n=m/M but i do not know number of moles.

PS: This is my own revision and not homework. I have a University exam on monday and am struggling loads with thermodynamics. I feel I am missing a lot of the equations i should need, does anyone have a link to a list of them? The material my lecturers gave me is not very helpful.

Thanks
Any help appreciated

Nathan

2. Apr 21, 2010

### Andrew Mason

Try PV = nRT

AM

3. Apr 21, 2010

### MrNathan

what is n though? is this not a constant? i am not given it in the question

4. Apr 21, 2010

### MrNathan

Oh i see, use pv = nRT to work out n.

ok, so from n = PV/RT, am i right in assuming the values of p, V and T are the differences?

n = pV/RT so n = (2850000 x 3)/(8.314 x 35)
n = 29382.45

m = nM so m = 851150.9

Im sure this is wrong as it seems too large.

5. Apr 21, 2010

### Andrew Mason

You have to be careful of the units. 1.5 bar is 150 kPa = 150000 N/m^2

Temperature has to be in Kelvin: 25 C = 298 K

So:

$$n = \frac{PV}{RT} = \frac{150000 \times 3}{8.314 \times 298} = 181.6 \text{moles}$$